1 Introduction

Since the beginning of the COVID-19 epidemic, policy makers in different countries have introduced different political action to contrast the contagion. The containment restrictions span from worldwide curfews, stay-at-home orders, shelter-in-place orders, shutdowns/lockdowns to softer measures and stay-at-home recommendations and including in addition the development of contact tracing strategies and specific testing policies. The pandemic has resulted in the largest amount of shutdowns/lockdowns worldwide at the same time in history.

The timing of the different interventions with respect to the spread of the contagion both at a global and intra-national level has been very different from country to country. This, in combination with demographical, economic, health-care related and area-specific factors, have resulted in different contagion patterns across the world.

Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.

Therefore, our goal is two-fold. The aim is to measure the effect of the different political actions by analysing and comparing types of actions from a global perspective and, at the same time, to benchmark the effect of the same action in an heterogeneous framework such as the Italian regional context.

In doing so, some issue arises concerning the identification and codification of the different measures undertaken by governments, the analysis related to whether a strategies resemblance can be detected across countries and the measurement of the effects of containment policies on contagion. Thus, after an introductory section explaining data and variables, a second section regards some explanatory analysis facing the codification of containment policies and the strategies resembling patterns. The third section deals with the measurement of policies effect from a global perspective, lastly the forth section analyze Italian lockdown and regional outcomes. Conclusion are drawn in the last section.

#Data and Variables

The data repositories used for this project are COVID-19 Data Repository by the Center for Systems Science and Engineering (CSSE) at Johns Hopkins University1 for contagion data (Dong, Du, and Gardner (2020)), and Oxford COVID-19 Government Response Tracker (OxCGRT)2 for policies tracking (Thomas et al. (2020)), together with World Bank Open Data Repository for demographic data.

Contagion data..

The Oxford COVID-19 Government Response Tracker (OxCGRT) collects all the containment policies adopted by government worldwide by making available information on 11 indicators of government containment responses of ordinal type. These indicators measure policies on a simple scale of severity / intensity and are reported for each day a policy is in place, specifying if they are “targeted”, applying only to a sub-region of a jurisdiction, or a specific sector; or “general”, applying throughout that jurisdiction or across the economy.

The containment ordinal variables considered are:

2 Containment strategies and resembling patterns

Identification and codification of different measures undertaken by governments performed by University of Oxford results in 11 ordinal variables selected as lockdown policies. This sets up the necessity to analyze and to aggregate them in a synthetic way in order to find out whether specific combinations of those policies making up political strategies come out to have a resemblance pattern across countries.

Therefore, we performed a Principal Component Analysis based on the polychoric correlation. It allows to estimate the correlation between two theorised normally distributed continuous latent variables, from two observed ordinal variables. It has no closed form but it is estimated via MLE assuming the two latent variables follows a bivariate normal density.

The interpretation of the first three principal components (accounting for the 80% of total variance) appears to be clear (see Figure ): the first one is closely related with freedom of movements and gathering restrictions together with information campaigns strategy, crucial in cases of draconian measures, the second one is related with the strategy of informing and testing the population, lastly the third one is related to informing and contact tracing the population. Summarizing, on one hand a first containment strategy aims at social distancing the entire population, on the other hand a second one aims at act locally and rapidly detect and isolate the positive cases, with two (alternative or complementary) tools: tracing contacts of infected and/or blanket population testing.

3 Containment strategies and resembling patterns

4 Effect of policies from a global perspective

Some countries have underestimated the dangerousness of the Coronavirus disease 2019 (COVID-19) and the importance of applying the containment measures. The little concern of some countries regarding the COVID-19 infectious disease is due to many and different reasons. Some countries decided to save the economy instead of people’s lives, as method to respond a war; in this case, a pandemic war.

For that, we want to analyze which countries adopt the ``optimal’’ policy measures to contain the contagion of COVID-19. Thanks to the Thomas et al. (2020) data sets, we know which type of measures each government takes and when. The indicators of government response considered are \(17\) in total, that can be resumed in indicators of a lockdown/social distancing, contact tracing, movement restrictions, testing policy, public health measures, and governance and socio-economic measures.

Therefore, some variables as the size of population are considered from the World Bank Open Data to have some additional covariates that can influence the variation in government responses to COVID-19.

We restrict the full range of responses to COVID-19 from governments around the countries analyzed in Section 3, i.e., Korea, Singapore, Germany, Canada, Sweden, Greece, Portugal, Spain, United States of America, Irland, United Kingdom, Italy, Netherlands, Austria, Switzerland, Finland, Norway, Denmark, and France.

The daily number of active persons is analyzed as a measure of the COVID-19 situation, i.e., the number of confirmed minus the number of deaths minus the number of recovered. Being a count variable, we decide to use a Negative Binomial Regression correcting also for the possible overdispersion. Therefore, the hierarchical structure is induced by the nested structure of countries inside the clusters and by the statement of the repeated measure. For that, we decide to use a generalized mixed model with family negative binomial. The country, clusters and date’s information are supposed to be used as random effects in the model.

So, the aim is to understand how the lockdown policies influence the number of active people. The observations are aligned concerning the first active case across the countries to have observations directly comparable from a longitudinal point of view. We have the following situation:

We can note the temporal variability between countries, clusters, as confirmation about the decision to use the mixed model.

4.1 Exploratory Analysis

The set of confounders considered in this analysis can be divided into three main areas:

  1. Longitudinal economic variables from Thomas et al. (2020);

  2. Longitudinal health system variables from Thomas et al. (2020);

  3. Fixed demographic/economic/health variables from the World Bank Open Data.

4.1.1 Economic Variables

We analyze four economic variables from Thomas et al. (2020):

Name Measurement Description
Income Support Ordinal Government income support to people that lose their jobs
Debt/contract relief for households Ordinal Government policies imposed to freeze financial obligations
Fiscal measures USD Economic fiscal stimuli
International support USD monetary value spending to other countries

We combine these two first economic variables into one continuous variable using the Polychoric Principal Component Analysis, to diminish the number of covariates inside the model, having \(9\) ordinal policies lockdown covariates.

The Economic PCA has a temporal pattern, with larger variabily near the last days of observatios. Korea and Singapore’s population received few money from the government respect to the other countries. The European ones are the best as finacial support to the population.

Therefore, the USD’s two economic variables are examined and transformed into a logarithmic scale to de-emphasize very large values.

The fiscal measure and international support variables have a large within-clusters variability. As we will see, these two variables will not enter into the final model.

For further details about the definition of the economic variables, please see the BSG Working Paper Series.

4.1.2 Demographic/Fixed variables

We analyze various variables from the World Bank Open Data that are fixed along the temporal dimension:

Name Measurement
Population Numeric
Population ages 65 and above (% of total population) Numeric
Population density (people per sq. km of land area) Numeric
Hospital beds (per 1,000 people) Numeric
Death rate, crude (per 1,000 people) Numeric
GDP growth (annual %) Numeric
Urban population (% of total population) Numeric
Surface area (sq. km) Numeric

Korea and Singapore seems to be the two yougest countries, it could be a reason about their low number of active person during the pandemic period.

The population density of the first Cluster seems weired, it is due by the Singapore situation. Probably, the hospital beds are directly relationated.

Another time the Singapore situation is clear analyzing the first Cluster. We have a large density population, so low surface area respect the countries of the other clusters.

4.1.3 Health variables

We analyze two heatlh systems variables.

Name Measurement Description
Emergency Investment in healthcare USD Short-term spending on, e.g, hospitals, masks, etc
Investment in vaccines USD Announced public spending on vaccine development 
FALSE Scale for 'x' is already present. Adding another scale for 'x', which will
FALSE replace the existing scale.
FALSE Scale for 'x' is already present. Adding another scale for 'x', which will
FALSE replace the existing scale.

Also, in this case, we transform the set of healthy variables into one continuous variable using the Polychoric Principal Component Analysis.

FALSE Scale for 'x' is already present. Adding another scale for 'x', which will
FALSE replace the existing scale.

4.2 Model

Also, we lag the number of active respect to \(14\) days, considering the influences of the restrictions imposed at time \(t\) on the number of active at time \(t+14\), to make a correct impact.

The data are observed for each country nested within the temporal date. We are also considering the Clusters variable. Therefore we have a three-level structure of the data. The variability of the data comes from nested sources: countries are nested within clusters where the measures of the observations are repeated across time, i.e., longitudinal data.

For that, the mixed model approach is considered to exploit the different types of variability coming from the hierarchical structure of our data. Firstly, the Intraclass correlation coefficient (ICC) is computed:

\[ ICC_{date; active} = 0.0936 \quad ICC_{Countries; Active} = 0.4015 \quad ICC_{Clusters; Active} = 0.0951 \]

Therefore, the \(40.15\%\) of the data’s variance is given by the random effect of the countries, while the \(9.36\%\) by the temporal effect and \(9.51\%\) by the clusters effect. Therefore, the mixed model impose of sure a random effect for the countries; the other two effects is selected using the conditional AIC.

The random effects are used to model multiple sources of variations and subject-specific effects, and thus avoid biased inference on the fixed effects. The dependent variable is the cumulated number of active persons; therefore, a count data model is considered. To control the overdispersion of our data, i.e., the conditional variance exceeds the conditional mean, the negative binomial regression with Gaussian-distributed random effects is performed using the glmmTMB R package developed by Brooks et al. (n.d.). Let \(n\) countries, and country \(i\) is measured at \(n_i\) time points \(t_{ij}\). The active person \(y_{ij}\) count at time \(t+14\), where \(i=1,\dots, n\) and \(j = 1, \dots,n_i\), follows the negative binomial distribution:

\[y_{ij} \sim NB(y_{ij}|\mu_{ij}, \theta) = \dfrac{\Gamma(y_{ij}+ \theta)}{\Gamma(\theta) y_{ij}!} \cdot \Big(\dfrac{\theta}{\mu_{ij} + \theta}\Big)^{\theta}\cdot \Big(\dfrac{\mu_{ij}}{\mu_{ij} + \theta}\Big)^{y_{ij}}\] where \(\theta\) is the dispersion parameter that controls the amount of overdispersion, and \(\mu_{ij}\) are the means. The means \(\mu_{ij}\) are related to the host variables via the logarithm link function:

\[\log(\mu_{ij}) = \log(T_{ij}) + X_{ij} \beta + Z_{ij} b_i \quad b_i \sim \mathcal{N}(0,\psi)\]

where \(\log(T_{ij})\) is the offset that corrects for the variation of the count of the active person at time \(t\). \(\text{E}(y_{ij}) = \mu\) and \(\text{Var}(y_{ij}) = \mu (1 + \mu\phi)\) from Hardin and Hilbe (2018).

After some covariates selection steps and random effects selection, the final model returns these estimations for the fixed effects:

Estimate Std. Error z value Pr(>|z|)
(Intercept) -0.012 0.326 -0.035 0.972
pca_EC -0.547 0.070 -7.791 0.000
pop_density_log 0.103 0.031 3.354 0.001
pca_hs 0.053 0.020 2.607 0.009
workplace_closingF1 -0.290 0.138 -2.108 0.035
workplace_closingF2 -1.191 0.134 -8.902 0.000
workplace_closingF3 -0.513 0.170 -3.021 0.003
gatherings_restrictionsF1 -0.506 0.162 -3.120 0.002
gatherings_restrictionsF2 -1.259 0.141 -8.945 0.000
gatherings_restrictionsF3 -1.519 0.173 -8.804 0.000
gatherings_restrictionsF4 -1.702 0.179 -9.513 0.000
transport_closingF1 -0.056 0.106 -0.527 0.598
transport_closingF2 -0.501 0.198 -2.529 0.011
stay_home_restrictionsF1 -0.057 0.109 -0.528 0.598
stay_home_restrictionsF2 -0.111 0.148 -0.751 0.453
stay_home_restrictionsF3 -0.824 0.292 -2.826 0.005
testing_policyF1 0.216 0.091 2.376 0.017
testing_policyF2 0.558 0.113 4.945 0.000
testing_policyF3 1.349 0.158 8.544 0.000
contact_tracingF1 0.196 0.083 2.369 0.018
contact_tracingF2 0.360 0.095 3.784 0.000
ClustersCl2 1.461 0.173 8.454 0.000
ClustersCl3 1.955 0.158 12.377 0.000
ClustersCl4 2.365 0.148 16.029 0.000
ClustersCl5 2.403 0.159 15.122 0.000

and the variance for the random effects are equals:

Variance
Country 0.283
Date 4.320

The marginal \(R^2\), i.e., the variance explained by the fixed effects, equals \(0.28\), while the conditional one, i.e., the variance explained by the entire model, including both fixed and random effects, equals \(0.89\) considering the lognormal approximation Nakagawa and Schielzeth (2013).

Therefore, the model seems correctly formulated. Then, the main aim is to understand .

We will analyze the effects related to the following variables:

  1. Fixed effect of the lockdown policies;

  2. Fixed effect of the clusters;

  3. Fixed effect of the combination between lockdown policies and clusters;

  4. Random effect of the countries;

4.2.1 LOCKDOWN POLICIES

FALSE Scale for 'colour' is already present. Adding another scale for 'colour',
FALSE which will replace the existing scale.
FALSE Scale for 'colour' is already present. Adding another scale for 'colour',
FALSE which will replace the existing scale.

4.2.2 CLUSTERS

4.2.3 INTERACTION LOCKDOWN POLICIES AND CLUSTERS

4.2.3.1 Testing policies

4.2.3.2 Contact Tracing

4.2.3.3 Gatherings Restrictions

4.2.3.4 Stay Home Restrictions

4.2.3.5 Workplace Closing

4.2.3.6 Transport Closing

4.2.4 COUNTRIES

4.3 To sum up

5 Italian lockdown and regional outcomes

6 Supplementary materials

All the codes used for this analysis is available on Github. The report was written by rmarkdown, fully reproducible. You can find the rmakrdown file in Github.

References

Brooks, M. E., K. Kristensen, K. J. van Benthem, A. Magnusson, C. W. Berg, A. Nielsen, H. J. Skaug, M. Mächler, and B. Bolker. n.d. “GlmmTMB Balances Speed and Flexibility Among Packages for Zero-Inflated Generalized Linear Mixed Modeling.” The R Journal 9 (2): 378–400.

Dong, E., H. Du, and L. Gardner. 2020. “An Interactive Web-Based Dashboard to Track Covid-19 in Real Time.” Lancet Infect Dis.

Hardin, J. W., and J. M. Hilbe. 2018. Generalized Linear Models and Extensions. 4th ed. Stata Press.

Nakagawa, S., and H. Schielzeth. 2013. “A General and Simple Method for Obtaining \(R^2\) from Generalized Linear Mixed‐effects Models.” Methods in Ecology and Evolution 4 (2): 133–42.

Thomas, H., S. Webster, A. Petherick, T. Phillips, and B. Kira. 2020. “Oxford Covid-19 Government Response Tracker, Blavatnik School of Government.” Data Use Policy: Creative Commons Attribution CC BY Standard.

  1. https://github.com/CSSEGISandData/COVID-19/tree/master/csse_covid_19_data↩

  2. https://github.com/OxCGRT/covid-policy-tracker↩